Article by Georges Lafaye in

1. A branch of a stake in an entrenchment. This meaning is based on a passage of Livy known from a single manuscript, the reading of which has seemed suspect, perhaps wrongly so. Radii may well have been the proper designation for the sharp entangled branches, the spikes that bristled on the stipites and the valli in the palisades of Roman camps [vallum].2

2. The wand or pointer used by professors to bring a point, a line, or a drawing to the attention of their students (fig. 5217). It was especially useful to astronomers in the study of the celestial sphere; it thus was made one of their chief attributes, as is attested by a painting from Pompeii depicting the muse Urania (fig. 5912).3 The radius was used by astronomers, geographers, mathematicians, geometricians to draw their numbers and figures on the surface of the sand that filled the abacus [abacus, I],4 so that "sand and pointer, pulvis et radius" are for Cicero the very insignia of their profession. When the ancients brought to mind a Conon, a Euclid or an Archimedes, they always saw them radius in hand.5

Fig. 5912. — Pointer.

3. A shuttle (κερκίς), a small sharp stick around which the weaver winds the thread of the weft to pass it thru the warp [textrinum].6

The Author's Notes:

1
Perhaps derived from Greek ῥάβδος, which has about the same range of meanings; Bréal and Bailly, Dict. étym. lat.s.v.; synonym virga in Serv. ad Virg. Ecl.III.40.

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2Acuti aliusque per alium immissi radii,
Liv. XXXIII.5.11; the radii of codex Bambergensis (B) has been emended to rami by Madvig, Emend. Livianae2 (1877), an emendation followed ad loc. by Weissenborn.